Bio-oil is not considered to be toxic and is a product designed for topical use and not be ingested. Be aware, however, if you use it on your dog, it is highly likely that he will lick it off and end up ingesting it. As bio-oil is a petroleum-based product, ingesting it can lead to an upset stomach, diarrhea, and excessive water consumption, and you may see your dog eating grass in an attempt to cause vomiting that will get it out of his stomach.
If you have been using bio-oil on your dog, consider finding a product that is intended for use on animals. If you believe your dog has ingested bio-oil, you should contact your vet. He may ask you to bring your pup in for a full examination including blood tests to ensure he has not ingested toxic amounts that could lead to further medical problems.
Choose products made specifically for use on dogs that do not include BHT or mineral oil in their ingredients. There are natural organic products that contain glycine max seed oil, Melaleuca cajuputi oil, or Elaeis guineensis seed oil. All of these oils are easily absorbed through the skin without leaving any residue behind and have been proven to be very effective in helping your dog's skin to heal.
The bottom line is that the risks of using Bio-Oil on your dog far outweigh any possible benefits of its use. More importantly, before you use any skin care products on your dog, consult with your vet to make sure they are safe.